Such a pump and such an appliance are known from EP-A-0 463 992. The known appliance is a shaver having a holder with a shaving liquid and a pump for pumping the shaving liquid from the holder to a discharge opening of the shaver. The known pump comprises a central tubular element around which a bellows is arranged, an inlet valve being arranged at one end of the tubular element and an outlet valve being arranged at the other end of this element. A drawback of the known pump is that it comprises a comparatively large number of parts. Another drawback is that the dimensions of the pump are large in relation to the corresponding dimensions of the appliance and the holder.